Preparation - In a heavy saucepan, beat the eggs, 1/2 cup sugar, and flour together. Gradually mix the scalded milk into the egg mixture. Cook over medium heat, stirring constantly for about 5 minutes or until thickened. Remove from heat; stir in the butter and vanilla until well blended. Cover the surface of the filling with plastic wrap; let cool.

When cool, slice the bananas. Fold the sliced bananas into the filling. Spoon the mixture into a pre-baked pie shell. Top with whipped cream or whipped topping.